On the limit cycles of the Floquet differential equations

We provide sufficient conditions for the existence of limit cycles for the Floquet differential equations x˙(t) = Ax(t) + ε(B(t)x(t)+b(t)), where x(t) and b(t) are column vectors of length n, A and B(t) are n×n matrices, the components of b(t) and B(t) are T-periodic functions, the differential equa...

Descripción completa

Detalles Bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Rodrigues, Ana|||0000-0003-4775-0127
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:150741
Acceso en línea:https://ddd.uab.cat/record/150741
https://dx.doi.org/urn:doi:10.3934/dcdsb.2014.19.1129
Access Level:acceso abierto
Palabra clave:Averaging theory
Floquet differential equation
Limit cycles
Periodic solutions
Descripción
Sumario:We provide sufficient conditions for the existence of limit cycles for the Floquet differential equations x˙(t) = Ax(t) + ε(B(t)x(t)+b(t)), where x(t) and b(t) are column vectors of length n, A and B(t) are n×n matrices, the components of b(t) and B(t) are T-periodic functions, the differential equation x˙(t) = Ax(t) has a plane filled with T-periodic orbits, and ε is a small parameter. The proof of this result is based on averaging theory.